more than 2000 years we have believed in a Euclidean space, because certain experiments favoured it; but there is now reason to believe that these same experiments when pushed to greater accuracy decide in favour of a slightly different space (in the neighbourhood of massive bodies). The relativist sees no reason to change the rules of the game because the result does not agree with previous anticipations. Accordingly when he speaks of space, he means the space revealed by measurement, whatever its geometry. He points out that this is the space with which physics is concerned; and, moreover, it is the space of everyday perception. If his right to appropriate the term space in this way is challenged, he would urge that this is the sense in which the term has always been used in physics hitherto; it is only recently that conservative physicists, frightened by the revolutionary consequences of modern experiments, have begun to play with the idea of a pre-existing space whose properties cannot be ascertained by experiment—a metaphysical space, to which they arbitrarily assign Euclidean properties, although it is obvious that its geometry can never be ascertained by experiment. But the relativist, in defining space as measured space, clearly recognises that all measurement involves the use of material apparatus; the resulting geometry is specifically a study of the extensional relations of matter. He declines to consider anything more transcendental.
My second point is that since natural geometry is the study of extensional relations of natural objects, and since it is found that their space-order cannot be discussed without reference to their time-order as well, it has become necessary to extend our geometry to four dimensions in order to include time.
